The simplest definition of the Phrasal Verb category of expressions is contained in the heading of the PV forum. It is a verb whose meaning is modified by addition of one or more prepositions, pronouns, adverbs, particles etc. to form a phrase of an idiomatic character, often showing deep alteration of the original meaning of the verb.
Example: the meaning of take off (an overcoat, shoes, etc.) is pretty obvious, however the idiomatic 'take off' means the act of an airplane's departure from the ground (as opposite to 'land').
Example: when you say 'Put that book down and listen to me, will you', the phrase 'put down' is pretty self-explanatory. On the other hand, you can use the same collocation 'put' + 'down' to refer to an act of killing an animal because of an incurable disease or an injury it suffers from. ('So badly were the horse's hind legs crushed that the poor animal had to be put down')
Generally phrasal verbs constitute a vital component of everyday informal spoken language. Actually many phrasals are an informal replacement for their more 'sophisticated' counterpart.
The firemen managed to put out the fire at the shopping mall in no time.
(put out = extinguish)
I think the meeting should be put off till the next week.
(put off = postponed)
In a vast majority of cases, unless you know a given phrasal, you won't be able to deduce its meaning. If you know the meaning of 'set up' (organise, found, prepare for operation), it does not automatically give you any idea of the meaning of 'set down' (express).
Many fair-sized volumes have been written about phrasal verbs and their usage. I've just made a very superficial introduction to the topic. A lot can (and certainly will) be added. I hope I've given you an idea what the PV are all about and what to expect while studying them :? .
All the best - Tee Kay